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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

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[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
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k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
J
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k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
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greatest volume
hzbrl   3
N 28 minutes ago by hzbrl
Source: purple comet
A large sphere with radius 7 contains three smaller balls each with radius 3 . The three balls are each externally tangent to the other two balls and internally tangent to the large sphere. There are four right circular cones that can be inscribed in the large sphere in such a way that the bases of the cones are tangent to all three balls. Of these four cones, the one with the greatest volume has volume $n \pi$. Find $n$.
3 replies
hzbrl
May 8, 2025
hzbrl
28 minutes ago
J
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3 var inequality
SunnyEvan   4
N 29 minutes ago by SunnyEvan
Let $ a,b,c \in R $ ,such that $ a^2+b^2+c^2=4(ab+bc+ca)$Prove that :$$ \frac{7-2\sqrt{14}}{48} \leq \frac{a^3b+b^3c+c^3a}{(a^2+b^2+c^2)^2} \leq \frac{7+2\sqrt{14}}{48} $$
4 replies
SunnyEvan
Yesterday at 1:05 PM
SunnyEvan
29 minutes ago
J
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an exponential inequality with two variables
teresafang   7
N 30 minutes ago by teresafang
x and y are positive real numbers.prove that [(x^y)/y]^(1/2)+[(y^x)/x]^(1/2)>=2.
sorry.I’m not good at English.Also I don’t know how to use Letax.
7 replies
teresafang
May 4, 2025
teresafang
30 minutes ago
J
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3-var inequality
sqing   1
N an hour ago by sqing
Source: Own
Let $ a, b, c\geq 0,a^2+b^2+c^2=2 $. Prove that
$$ab+bc+ca+a+b+c- 3abc \leq 3$$$$ab+bc+ca-a-b-c-\frac{21}{20} abc \leq -1$$$$ab+bc+ca+a+b+c- \frac{5}{2}abc \leq \frac{2(9+2\sqrt 6)}{9}$$Let $a, b, c$ be real numbers such that $a^2+b^2+c^2=2$. Prove that
$$ ab+bc+ca-2abc\leq \frac{2(9+2\sqrt 6)}{9}$$
1 reply
sqing
an hour ago
sqing
an hour ago
J
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No math to big math in 42 days
observer04   2
N an hour ago by Ruegerbyrd
CAN IT BE DONE





usajmo
2 replies
observer04
5 hours ago
Ruegerbyrd
an hour ago
J
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[TEST RELEASED] OMMC Year 5
DottedCaculator   73
N an hour ago by Ruegerbyrd
Test portal: https://ommc-test-portal-2025.vercel.app/

Hello to all creative problem solvers,

Do you want to work on a fun, untimed team math competition with amazing questions by MOPpers and IMO & EGMO medalists? $\phantom{You lost the game.}$
Do you want to have a chance to win thousands in cash and raffle prizes (no matter your skill level)?

Check out the fifth annual iteration of the

Online Monmouth Math Competition!

Online Monmouth Math Competition, or OMMC, is a 501c3 accredited nonprofit organization managed by adults, college students, and high schoolers which aims to give talented high school and middle school students an exciting way to develop their skills in mathematics.

Our website: https://www.ommcofficial.org/
Our Discord (6000+ members): https://tinyurl.com/joinommc

This is not a local competition; any student 18 or younger anywhere in the world can attend. We have changed some elements of our contest format, so read carefully and thoroughly. Join our Discord or monitor this thread for updates and test releases.

How hard is it?

We plan to raffle out a TON of prizes over all competitors regardless of performance. So just submit: a few minutes of your time will give you a great chance to win amazing prizes!

How are the problems?

You can check out our past problems and sample problems here:
https://www.ommcofficial.org/sample
https://www.ommcofficial.org/2022-documents
https://www.ommcofficial.org/2023-documents
https://www.ommcofficial.org/ommc-amc

How will the test be held?/How do I sign up?

Solo teams?

Test Policy

Timeline:
Main Round: May 17th - May 24th
Test Portal Released. The Main Round of the contest is held. The Main Round consists of 25 questions that each have a numerical answer. Teams will have the entire time interval to work on the questions. They can submit any time during the interval. Teams are free to edit their submissions before the period ends, even after they submit.

Final Round: May 26th - May 28th
The top placing teams will qualify for this invitational round (5-10 questions). The final round consists of 5-10 proof questions. Teams again will have the entire time interval to work on these questions and can submit their proofs any time during this interval. Teams are free to edit their submissions before the period ends, even after they submit.

Conclusion of Competition: Early June
Solutions will be released, winners announced, and prizes sent out to winners.

Scoring:

Prizes:

I have more questions. Whom do I ask?

We hope for your participation, and good luck!

OMMC staff

OMMC’S 2025 EVENTS ARE SPONSORED BY:

[list]
[*]Nontrivial Fellowship
[*]Citadel
[*]SPARC
[*]Jane Street
[*]And counting!
[/list]
73 replies
DottedCaculator
Apr 26, 2025
Ruegerbyrd
an hour ago
J
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3-var inequality
ys-lg   0
an hour ago
$x,y,z>0.$ Show that $x^2+y^2+z^2+xyz+2\ge 2(xy+yz+zx).$
0 replies
ys-lg
an hour ago
0 replies
J
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Number theory
EeEeRUT   4
N an hour ago by EeEeRUT
Source: Thailand MO 2025 P10
Let $n$ be a positive integer. Show that there exist a polynomial $P(x)$ with integer coefficient that satisfy the following
[list]
[*]Degree of $P(x)$ is at most $2^n - n -1$
[*]$|P(k)| = (k-1)!(2^n-k)!$ for each $k \in \{1,2,3,\dots,2^n\}$
[/list]
4 replies
EeEeRUT
May 14, 2025
EeEeRUT
an hour ago
J
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Essentially, how to get good at olympiad math?
gulab_jamun   1
N an hour ago by Konigsberg
Ok, so I'm posting this as an anynonymous user cuz I don't want to get flamed by anyone I know for my goals but I really do want to improve on my math skill.

Basically, I'm alright at computational math (10 AIME, dhr stanford math meet twice) and I hope I can get good enough at olympiad math over the summer to make MOP next year (I will be entering 10th as after next year, it becomes much harder :( )) Essentially, I just want to get good at olympiad math. If someone could, please tell me how to study, like what books (currently thinking of doing EGMO) but I don't know how to get better at the other topics. Also, how would I prepare? Like would I study both proof geometry and proof number theory concurrently or just study each topic one by one?? Would I do mock jmo/amo or js prioritize olympiad problems in each topic. I have the whole summer ahead of me, and intend to dedicate it to olympiad math, so any advice would be really appreciated. Thank you!
1 reply
gulab_jamun
5 hours ago
Konigsberg
an hour ago
J
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Central sequences
EeEeRUT   12
N 2 hours ago by Ihatecombin
Source: EGMO 2025 P2
An infinite increasing sequence $a_1 < a_2 < a_3 < \cdots$ of positive integers is called central if for every positive integer $n$ , the arithmetic mean of the first $a_n$ terms of the sequence is equal to $a_n$.

Show that there exists an infinite sequence $b_1, b_2, b_3, \dots$ of positive integers such that for every central sequence $a_1, a_2, a_3, \dots, $ there are infinitely many positive integers $n$ with $a_n = b_n$.
12 replies
EeEeRUT
Apr 16, 2025
Ihatecombin
2 hours ago
J
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Functional Equation from IMO
prtoi   3
N 2 hours ago by RevolveWithMe101
Source: IMO
Question: $f(2a)+2f(b)=f(f(a+b))$
Solve for f:Z-->Z
My solution:
At a=0, $f(0)+2f(b)=f(f(b))$
Take t=f(b) to get $f(0)+2t=f(t)$
Therefore, f(x)=2x+n where n=f(0)
Could someone please clarify if this is right or wrong?
3 replies
prtoi
Yesterday at 8:07 PM
RevolveWithMe101
2 hours ago
J
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inequality with roots
luci1337   0
2 hours ago
Source: an exam in vietnam
let $a,b,c\geq0: a+b+c=1$
prove that $\Sigma\sqrt{a+(b-c)^2}\geq\sqrt{3}$
0 replies
luci1337
2 hours ago
0 replies
J
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9 best high school math competitions hosted by a college/university
ethan2011   16
N 2 hours ago by aarush.rachak11
I only included college-hosted comps since MAA comps are very differently formatted, and IMO would easily beat the rest on quality since mathematicians around the world give questions, and so many problems are shortlisted, so IMO does release the IMO shortlist for people to practice. I also did not include the not as prestigious ones(like BRUMO, CUBRMC, and others), since most comps with very high quality questions are more prestigious(I did include other if you really think those questions are really good).
16 replies
ethan2011
Apr 12, 2025
aarush.rachak11
2 hours ago
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G, L, H are collinear
Ink68   3
N 2 hours ago by luci1337
Given an acute, non-isosceles triangle $ABC$. $B, C$ lie on a moving circle $(K)$. $(K)$ intersects $CA$ at $E$ and $BA$ at $F$. $BE, CF$ intersect at $G$. $KG, BC$ intersect at $D$. $L$ is the perpendicular image of $D$ with respect to $EF$. Prove that $G, L$ and the orthocenter $H$ are collinear.
3 replies
Ink68
4 hours ago
luci1337
2 hours ago
J
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J
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Preparation for the AIME
tzhang1   5
N Mar 28, 2011 by trigonometry456103
What chapter in the AoPS Volume 1 or volume2 book would help students develop the skills needed to solve problem #1-15 on the AIME 2011 I?
5 replies
tzhang1
Mar 28, 2011
trigonometry456103
Mar 28, 2011
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Preparation for the AIME
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Reveal topic tags
AMC
AIME
AIME I
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tzhang1
664 posts
tzhang1
#1 h  Mar 28, 2011, 10:49 PM • 2 Y
Y by Adventure10, Mango247
What chapter in the AoPS Volume 1 or volume2 book would help students develop the skills needed to solve problem #1-15 on the AIME 2011 I?
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VIPMaster
458 posts
VIPMaster
#2 h  Mar 28, 2011, 10:50 PM • 2 Y
Y by Adventure10, Mango247
Well, if your goal is to solve the entire AIME, I think you would need the entirety of both books. Sorry to be of no help at all, but your question is extremely vague and broad.
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trigonometry456103
349 posts
trigonometry456103
#3 h  Mar 28, 2011, 11:02 PM • 3 Y
Y by Adventure10, Mango247, and 1 other user
All of it!
:)

All of it might not even be enough......
But certainly improve your score by a significant amount(if used properly)
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Maxima
1012 posts
Maxima
#4 h  Mar 28, 2011, 11:12 PM • 2 Y
Y by Adventure10, Mango247
Well, he refers to 1-15 on the *2011* AIME. It most certainly is not all of it.
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VIPMaster
458 posts
VIPMaster
#5 h  Mar 28, 2011, 11:13 PM • 2 Y
Y by Adventure10, Mango247
...but still a substantial portion of it.
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trigonometry456103
349 posts
trigonometry456103
#6 h  Mar 28, 2011, 11:16 PM • 5 Y
Y by john456852, ThisUsernameIsTaken, Adventure10, Mango247, and 1 other user
That's true.
:)
In that case,
VOLUME 1:
Chapters 3, 4, 6, 7, 11-20, 28

VOLUME 2:
Chapters 1-4, 6, 9, 12, 13, 23, 26
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